7587 2019

April 2019

Rush hours and urbanization Tobias Seidel, Jan Wickerath

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CESifo Working Paper No. 7587 Category 4: Labour Markets

Rush hours and urbanization

Abstract We use a spatial general equilibrium model with potential commuting of workers between their place of work and their place of residence to analyze the effects of rush hours on the spatial allocation of employment and population, average labor productivity and the housing market. Abolishing traffic congestion during rush hours leads to a more urbanized economy as households move from the low-density countryside to the commuter belts of cities rather than from the city centers to the periphery. Employment, however, becomes more agglomerated in high-density large cities. This adjustment implies an increase of average labor productivity of 7.2 percent and higher inequality of housing costs.

JEL-Codes: R120, R130, R410.

Keywords: urbanization, commuting, traffic, congestion, spatial general equilibrium.

Tobias Seidel

University of Duisburg-Essen Lotharstr. 65

Germany – 47057 Duisburg tobias.seidel@uni-due.de

Jan Wickerath University of Duisburg-Essen

Lotharstr. 65 Germany – 47057 Duisburg jan.wickerath@uni-due.de

This version: March 2019

1 Introduction

Commuting to work during rush hours imposes a cost to workers. It does not only re-duce leisure, but also raises the stress level of individuals (Gottholmseder et al. 2009)and deteriorates individual health conditions (e.g. Kuenn-Nelen 2016). Kahnemanet al. (2004) shows that individuals rank commuting as the least satisfying activityof their daily routine. Redding and Turner (2015) documents for several developedcountries that the average employee commutes approximately 40 minutes per day.Importantly, however, it is not only the distance between home and work, but alsothe amount of traffic that determines commuting times. According to the INRIXGlobal Traffic Scorecard, estimates indicate that traffic jams account for up to onethird of commuting time. To provide a few examples, commuters in Rome lost 254hours in traffic congestion in 2018. Dublin (246), Paris (237) or London (227) arefurther examples of urban areas in this ranking.1

While commuting is costly, it also offers employees the opportunity to separatetheir place of residence from their place of work. Thereby, households can enjoylower housing costs in less dense places (e.g. in the countryside or the peripheryof cities) and high-paid jobs in economic centers at the same time. If commutingcosts fall short of the extra housing costs in cities and differences in amenities, thisworkplace-residence separation implies higher utility for the individual. Traffic jamsduring rush hours, however, distort the location decision. If commuting becomesmore costly, it might be more beneficial to look for housing closer to work at theexpense of higher prices. Alternatively, households might leave the area entirely andlocate in other less congested places of the economy.

To understand the economy-wide implications of rush hours, we use a spatial generalequilibrium model that allows individuals to migrate across locations and separatetheir place of work from their place of residence. Individuals consume a differentiatedtradable good and housing owned by immobile landlords. Rents adjust endogenouslyto changes in location-commuting decisions of workers and operate as a congestionforce in the model. We are particularly interested in how reductions in commutingtimes affect the population and employment shares in urban versus rural areas, theaverage productivity of labor and housing prices. We build on Monte, Redding, andRossi-Hansberg (2018), but extend their framework in two important ways. First,we model commuting in time units as in Ahlfeldt et al. (2015) with longer commut-ing times reducing welfare ceteris paribus. This allows us to use bilateral commutingtime between locations when we confront the model with data and to back out a

1See www.inrix.com/scorecard for details.

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commuting elasticity that indicates how households value one minute of additionalcommuting time in terms of utility. Second, we endogenize location-specific produc-tivity as in Allen and Arkolakis (2014). Productivity in each location depends onexogenous factors and increases in employment density, so changes in the spatialallocation of jobs affects location-specific and economy-wide average productivity(Combes et al. 2012). The latter is affected via two channels. First, average produc-tivity increases if workers substitute their job in a low-productivity region with onein a higher-productivity region. Second, productivity is positively associated withhigher employment density.

We calibrate the model for 412 German districts in 2010 using bilateral trade andcommuting flows as well as information on employment, population and house prices.In the baseline scenario, we retrieve bilateral commuting times between districts fromgoogle maps. We assume that the journey to work starts at 8 a.m. and that workersreturn at 5 p.m. In the counterfactual analysis, we eliminate traffic congestion bysubstituting the travel times during rush hours with those at 3 a.m. when thereare hardly any cars on the roads. Solving the model for a new spatial equilibriumdelivers answers to the above questions.

We find that the reduction in traffic congestion leads to a higher degree of overallurbanization in the economy – although commuting becomes relatively more at-tractive between urban centers and their less populated hinterland. The reason isthat workers leave the countryside to move to the periphery of economic centers.It is the combination of living there and commuting to the city that becomes moreappealing at the expense of low-density rural areas. While the city periphery expe-riences net immigration, employment clusters more intensively in high-productiveeconomic centers. These adjustments map to changes in relative housing costs withhighest increases in the commuter belts of cities and declines in remote places. Theagglomeration of jobs in cities and the reallocation of jobs from low-productivity tohigh-productivity locations implies an increase of average labor productivity of 7.2percent.

The policy implications of this quantitative framework suggest that investments incapacity-enhancing transport infrastructure generate a higher return in urban areasand their hinterland compared to the periphery. Although we know from the fun-damental law of road congestion (Duranton and Turner 2011) that additional roadcapacity has little impact on commuting times in equilibrium due to more drivingand migration to this region, the higher capacity of traffic infrastructure allows morepeople to commute. Therefore, such investments promise average productivity gains

2

due to higher economic density in line with our findings. However, we would expectthese gains to be quantitatively smaller, as the endogenous increase in traffic volumein those urban areas would act as an additional congestion force.

Our paper relates to several strands of literature. First, there exists a regional eco-nomics literature on traffic and transport infrastructure using both structural partialequilibrium estimations (e.g. Duranton and Turner 2011, Couture, Duranton, andTurner 2018 and Ahlfeldt and Feddersen 2018) and theoretical partial and generalequilibrium models (e.g. Rotemberg 1985, Anas 2012 and Anas and Pines 2013).Our model builds on a system of regions and sheds light on the productivity andallocation effects of rush hours. Second, we build our analysis on recent advance-ments in spatial general equilibrium theory (e.g. Allen and Arkolakis 2014, Allenand Arkolakis 2019, Redding 2016, Redding and Rossi-Hansberg 2017 and Behrenset al. 2017) where locations are connected via labor mobility and goods trade. Forour research question, it is essential to allow for commuting and thus a possibleseparation of place of work and place of residence. We therefore combine Monte,Redding, and Rossi-Hansberg (2018) with Ahlfeldt et al. (2015) to model commut-ing in time units. Fretz, Parchet, and Robert-Nicoud (2017) use a similar model toestimate the effect of highway connections in Switzerland on local labor markets.Heblich, Redding, and Sturm (2018) combine commuting decisions of householdswith the introduction of the steam railway in the mid-19th century in London toexplain the growth in economic density in the city of London during that time.

Third, traffic congestion represents a friction for the spatial allocation of economicactivity that leads to spatial misallocation of resources (Hsieh and Klenow 2009).Our results are qualitatively similar to Hsieh and Moretti (2018) showing that strin-gent housing supply regulation reduces growth as it restricts access to highly pro-ductive cities and Hsieh et al. (2018) analyzing the effect of skill mismatches.

In the remainder of the paper, we start in section 2 with a detailed expositionof the model, explain the calibration procedure in section 3 and finally run thecounterfactual exercise and discuss our findings in section 4.

2 Model

Consider an economy with regions n, i ∈ N and Lmobile workers. While each workersupplies one unit of labor inelastically, migration makes labor supply elastic fromthe perspective of regions. Importantly, workers are able to choose their locations ofwork and residence separately, so we distinguish between workers (Ln) and residents

3

(Rn) in each location n. If the place of work differs from the place of residence,individuals need to commute. This comes at the cost of less leisure time and reducesutility. Apart from labor mobility and commuting, regions are also connected viacostly trade of varieties of a differentiated consumption good Q. Each region inthe economy is further endowed with developable land for housing that is owned byimmobile landlords who consume where they live. The market for land is perfectlycompetitive.

2.1 Workers

The utility of a worker ω living in region n and working in region i is given by

Uniω =bniωκni

(Qnωα

)α ( Hnω1− α

)1−α, (1)

where Qnω denotes the quantity of a tradable differentiated good, Hnω representsconsumption of housing, κni captures bilateral commuting costs and bniω is a location-worker-specific amenity parameter. The Cobb-Douglas parameter 0 < α < 1 gov-erns the relative importance of the tradable good and housing for workers’ utility.The consumer good Q is composed of differentiated varieties according to a CES-aggregator of the form

Qnω =[∑i∈N

∫ Mi0

qni(j)σ−1σ dj

] σσ−1

,

where qni(j) denotes the quantity of variety j that is produced in region i andconsumed by a worker living in region n. Mi is the measure of firms located inregion i. We assume that varieties are imperfect substitutes with a correspondingconstant elasticity σ > 1.

Utility maximization implies that households dedicate fixed income shares α and1−α to the differentiated good and housing, respectively. Denoting by En aggregateexpenditure in location n, we have

Q∗nω =αEnPQ,n

H∗nω =(1− α)EnPH,n

,

where PQ,n is the price index of the composite good and PH,n denotes the price perunit of housing in region n. Region n′s demand for a variety j imported from i is

4

given by

qni(j) =pni(j)−σ

P 1−σQ,nαEn, (2)

with pni(j) denoting the corresponding consumer price. Notice that landownersspend their entire income on consumption goods such that total expenditure onQn equals PQ,nQn = (αv̄n + (1 − α)v̄n)Rn = v̄nRn with v̄n representing averageper-capita income in n.

We follow Ahlfeldt et al. (2015) in modeling commuting costs as a function of bi-lateral commuting times. In particular, we impose κni = τµni, where τni denotesbilateral commuting time and µ is a parameter describing the household’s distastefor commuting. We will back out the value of this parameter from data in the em-pirical analysis below. The negative relation between commuting and utility can bemotivated, for example, by the fact that commuting raises stress levels (e.g. Got-tholmseder et al. 2009), deteriorates health conditions (e.g. Kuenn-Nelen 2016) orthat workers dislike traveling to work (e.g. Kahneman et al. 2004).

Finally, we assume that individuals have heterogeneous preferences for combina-tions of locations for work and living. We follow (among others) Eaton and Kortum(2002), McFadden (1974) and Monte, Redding, and Rossi-Hansberg (2018) in mod-eling amenities bniω as random draws from a Fréchet distribution. Therefore, theircdf is given by Gni(b) = e−Bnib

−� , where Bni > 0 and � > 1. The scale parameterBni represents the average value of amenities from living in region n and workingin region i. Higher values of � imply a lower dispersion of the distribution. Indirectutility of worker ω living in n and earning her income in i then results as

U∗niω =bniωwi

κniPαQ,nP1−αH,n

, (3)

where wi is her labor income. Notice that indirect utility is a monotone transfor-mation of the amenity parameter, so it is also Fréchet distributed with Gni(U) =e−ΦniU

−� and Φni = Bni (κniPαnQ1−αn )−�w�i .

We use the property that the maximum of repeated draws from the Fréchet distri-bution is also Fréchet distributed to write the probability that a worker chooses tolive in location n and work in location i as

λni =ΦniΦ (4)

5

with Φ = ∑r

∑s

Φrs. By the law of large numbers, the probability of living in region nand working in region i should be equivalent to the share of workers living in n andworking in i, so that λni = Lni/L. As workers are regionally mobile, expected utilityneeds to be equalized in equilibrium for all residence-workplace combinations. Thismeans that

Ū = E[Uniω] = Φ1/�Γ(�− 1�

). (5)

We can write the probability that a worker commutes to region i given she lives inn as λni|n = Φni/

∑s

Φns. Further notice that we can express the measure of workersemployed in region i as Li =

∑nLni and the measure of workers living in region n by

Rn =∑iLni. Labor market clearing then implies that in every location i

Li =∑n

λni|nRn

must hold and the expected income conditional on living in location n is given by

v̄n =∑i

λni|nwi. (6)

2.2 Housing market

Land owners are immobile and they supply housing according to the aggregatesupply function

Hsn = H̄nP δH,n, (7)

where H̄n captures region-specific housing fundamentals such as developable land,natural constraints or regulation, and δ denotes the housing supply elasticity (Saiz2010).

From the household’s optimal housing demand above we can derive the aggregatedemand for housing in region n as

Hdn = (1− α)v̄nRnPH,n

. (8)

Hence, housing market clearing requires that

PH,n =(

(1− α) v̄nRnH̄n

) 11+δ

(9)

holds in every region.

6

2.3 Production and inter-regional trade

Firms employ labor as the only factor of production and operate under monopolisticcompetition and internal increasing returns to scale that stem from fixed costs fwi.This implies decreasing average costs so every firm manufactures a unique varietyj. To produce qi(j) units of variety j a firm needs to hire

li(j) = f +qi(j)Ai(Li)

laborers, where Ai(Li) = ĀiLνi describes location-specific productivity, which is afunction of the number of workers employed in that region. Therefore, productivityspillovers act as an agglomeration force in our model and the parameter ν governsthe strength of these spillovers (see e.g. Behrens and Robert-Nicoud 2015).

Shipping goods between regions i and n implies iceberg trade costs dni > 1 while wenormalize intra-regional trade costs to unity, dnn = 1. The profit-maximizing pricefor every destination market results as a constant mark-up over marginal costs,

pni(j) =σ

σ − 1dniwiAi(Li)

.

Free entry of firms drives down profits to zero implying li(j)∗ = σf , so total em-ployment in i, Li, determines the number of operating firms, Mi = Li/(σf), in thislocation.2

Against this background, we obtain the expenditure share spent on goods producedin region i as

πni ≡Mi p

1−σni∑

kMk p1−σnk

=L

1−(1−σ)νi

(widniĀi

)1−σ∑k L

1−(1−σ)νk

(wkdnkĀk

)1−σ . (10)We observe from (10) that πni is increasing in the number of varieties producedin region i, Mi, and decreasing in trade costs between regions n and i, dni. Thisnotation allows us to express region n′s price index for the composite good Q as

PQ,n =[∑i∈N

p1−σni

] 11−σ

= σσ − 1

(L1−(1−σ)νnσfπnn

) 11−σ wndnn

Ān. (11)

2We assume that firms are atomistic, i.e. they regard aggregate employment as given, ignoringthe effect that their labor demand has on total employment and hence productivity in their region.

7

2.4 Equilibrium

The equilibrium in this model is defined by a vector of six endogenous variables{wn, v̄n, Ln, Rn, PH,n, PQ,n}Nn=1 and a scalar Ū that solve the following equations:the price index (11), housing-market clearing (9), average income (6), the conditionthat income equals expenditure,

wiLi =∑n∈N

πniv̄nRn,

and aggregated probabilities of living and working in region n based on (4), that isλRn =

∑i λni and λLn =

∑i λin. Finally, the normalization of L determines the utility

level Ū via the labor-market clearing condition L = ∑n Ln.3 Data and calibration

3.1 Data

We calibrate the model to the German economy with its 412 districts using dataon average monthly gross labor earnings by place of work and by residential lo-cation, regional employment and residential information from the German FederalEmployment Agency for all German workers who are subject to social insurance con-tributions.3 Bilateral in- and out-commuting flows between districts are availablefrom the same source and for the same population of workers. Further, we use in-formation on land prices from the Federal Institute for Research on Building, UrbanAffairs and Spatial Development. Bilateral trade flows come from the Forecast ofNationwide Transport Relations in Germany (Verkehrsverflechtungsprognose 2030)provided by the Clearing House of Transport Data at the Institute of Transport Re-search of the German Aerospace Center. The data contain bilateral trade volumesin metric tons at the product level by transport mode (road, rail, water) betweenEuropean regions, where one German region is either exporter, importer or partof the trade route. As the most recent year for these data is 2010, this constraintdefines the year of the analysis. We relegate a more detailed description of thesedata sources to the appendix.

To get round trip commuting times τni, we feed regions’ centroids derived from GISsoftware into google maps and request two travel time matrices. For the baselinescenario, we assume that workers start their commute at eight o’clock in the morning

3Jurisdictions are equivalent to the EU’s NUTS-3 classification (Kreise and Kreisfreie Städte).

8

and return from work at five o’clock in the afternoon to capture traffic-congestedrush hours. To obtain congestion-free travel times, we repeat the same exercisefor three o’clock in the morning. Our commuting data only include cross-borderjourneys where 92 percent of workers choose the car as the mode of transport. Wetherefore ignore public transport as a mode of commuting. A limitation of ourdataset is that we only observe worker locations at the district level which does notallow us to infer intra-district commuting times. Rather than setting them to zero,we approximate these missing values by computing the weighted average of traveltimes from neighboring regions and take 20 percent of this value. If everybody wasliving on the region’s border, the value would be around 50 percent. We show inthe robustness section 4.4 below that our results are robust to alternative valuesbetween 0-40 percent.

Our data set contains a small number of workers who, if the data were taken literally,have round trip commuting times of over ten hours per day (see Figure 6 in theappendix). As we understand commuting as daily trips to work, we truncate thedistribution by allowing only round trip commuting times of less than 3 hours anddocument in the robustness section 4.4 below that our findings are not sensitiveto varying this threshold between 1-4 hours. Truncating at 3 hours includes 92.8percent of all cross-district commutes in Germany.

To develop an idea about the spatial commuting pattern, we plot average in-commutingtimes per district in Figure 1. Workers spend significantly less time on commuting inrural areas while economic centers like Munich, Stuttgart, Frankfurt or Cologne andDusseldorf are characterized by average in-commuting times of up to 80 minutes.Table 1 underlines these regional disparities by reporting the top-5 and bottom-5districts or cities ranked by the average in-commuting times. We further observethat high in-commuting is driven to a remarkable extent by higher traffic congestion.In the top-5 districts, commuters spend up to 38 percent of their time in traffic jamswhile in the bottom-5 districts this ratio ranges only between 12-17 percent.4

3.2 Calibration

We now bring the model to data. First, we use the commuting data to obtain bilat-eral commuting shares, λni, and the conditional commuting share, λni|n. Togetherwith information on location-specific employment, Li, labor-market clearing con-ditions Li =

∑n λni|nRn allow us to back out the number of residents in region n.

4See also Figure 7 in the appendix.

9

Figure 1: Average in-commuting time per district

Notes: In-commuting times are weighted by the shares of in-commuters from other districts.

Notice that we use equilibrium conditions from the model to determine Rn instead ofusing available data on residents to ensure that the model is consistent. In a similarvein, we combine conditional employment shares with observed wages by place ofwork, wi, to determine average labor income in region n, v̄n =

∑iλni|nwi. Relating

these model predictions for v̄n and Rn to observed data in panels (a) and (b) ofFigure 2 documents a good model fit. We observe that our predictions for localpopulation are centered about the actual values and deviations are relatively small(within ±6%). For average residential income, our model predicts slightly lowervalues, but the relationship still turns out strong. Overall, this is a first assurancethat our model describes the spatial economy well.

Housing fundamentals, H̄n. We use data on land prices as a measure of housing

10

Table 1: Commuting times and time spent in traffic

∅ in-commutingtime, minutes

∅ time in traffic,minutes

∅ % in traffic

Top 5

Munich (district) 82 25 30%Frankfurt 67 23 34%Main-Taunus-Kreis 66 16 25%Dusseldorf 62 24 38%Munich (City) 58 19 33%

Bottom 5

Harz 9 1 14%Erzgebirgskreis 9 1 15%Southwest Palatinate 8 1 17%Garmisch-Partenkirchen 8 1 12%Goerlitz 7 1 13%

Notes: We sorted all districts in Germany by the average in-commuting time for workers. All numbers arerounded to the nearest integer.

prices PH,n and determine region-specific housing fundamentals, H̄n, from (9). Basedon the German Statistical Office (2015), households spend around one third of theirdisposable income on housing, so we set the expenditure share for consumption goodsto α = 0.7. As this expenditure includes energy and maintenance, we alternativelyuse a share of 20 percent in the robustness section 4.4 to show that the insights donot change qualitatively. Further, we follow Lerbs (2014) in choosing a value forthe housing supply elasticity δ = 0.38. Adding price data on developed land, PH,n,yields H̄n.

Fundamental productivity, Ān. To uncover the region-specific productivity fun-damentals, we first need to obtain estimates for unobserved bilateral trade frictions,dni. We do so by deriving a gravity equation from the model,

Qni = πniv̄nRn =Liσf

(σσ−1

widniAi

)1−σΩn

v̄nRnPQ,n

,

where Ωn ≡∑kMk p

1−σnk denotes a multilateral resistance term. Notice that the

left-hand side captures quantities rather than values as bilateral regional trade dataare only available in volumes. Taking logs on both sides delivers the estimation

11

Figure 2: Observed vs. predicted wages and employment

0.4 0.6 0.8 1.0Model prediction vn

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Obse

rved

val

ues

Panel (a)

0 5 10 15Model prediction Rn

0.0

2.5

5.0

7.5

10.0

12.5

15.0

17.5Panel (b)

Notes: We have normalized wages to range between zero and one. Employment is normalized to have a mean ofone.

equation

logQni = log Liσf

(wi σ

Ai (σ − 1)

)1−σ+ log( v̄nRnΩnPQ,n)

+ (1− σ) log dni

= χi + ξn − (σ − 1) log dni, (12)

where χi and ξn are exporter and importer fixed effects. To parameterize tradefrictions, we follow the gravity literature (e.g. Head and Mayer 2015) in assumingthat trade costs are a function of bilateral distance, a set of standard controls C andan error term,

dni = distψni eγC ẽni. (13)

Plugging this into (12) yields

logQni = χi + ξn − (σ − 1) ψ log distni + (1− σ)γC + (1− σ) log(ẽni). (14)

Imposing a value for the elasticity of substitution of σ = 4 (Broda and Weinstein2004), we are able to estimate ψ with ordinary least squares. The result deliv-ers bilateral trade frictions according to (13).5 Importantly, bilateral trade flows

5Note that the trade gravity can only be used to calibrate trade costs where distni > 0, i.e.

12

are available at the sector level which allows us to capture the price dimension byincluding sector fixed effects. Transforming these volume data into values by us-ing unit prices from COMTRADE delivers similar estimates of the trade elasticity(Henkel and Seidel 2019).

Table 2: Trade gravity estimation

log(Trade volume) (1) (2)

log(Distance) −1.259∗∗∗ −0.977∗∗∗(0.002) (0.004)

Dialect similarity 0.225∗∗∗(0.013)

Contiguity 0.524∗∗∗(0.009)

Same state 0.468∗∗∗(0.005)

Constant 3.035∗∗∗ 3.039∗∗∗(0.063) (0.063)

Sector dummies Yes Yes

Importer FE Yes Yes

Exporter FE Yes Yes

R2 0.402 0.408

Observations 1,116,832 1,116,832

Notes: ∗∗∗, ∗∗, ∗ denote significance at the 1-, 5-, and 10-percent level, respec-tively.

Table 2 summarizes the results of the trade gravity estimation. The estimated dis-tance elasticities of −0.98 and −1.26 are in line with the values usually found in thegravity literature. Head and Mayer (2015) find trade elasticities to be consistentlyin the area of −1. Having set σ = 4 implies a parametrization for ψ = 0.42 if webuild on column (2).

We are now equipped with the necessary information to back out location-specificproductivity levels.6 Substituting bilateral trade shares, (10), into the region-specificgoods market clearing conditions, wiLi =

∑n πniv̄nRn, delivers a system of N equa-

tions which can be solved for a unique vector of Ān, where we choose the parameter

n 6= i and Qni > 0. As trade costs are assumed to be of the iceberg form, we already know thatdistni = 0 =⇒ dni = 1. For the case where no bilateral trade is observed, i.e. Qni = 0, tradecosts are assumed to be prohibitively high, i.e. Qni = 0 ⇐⇒ dni =∞.

6See Monte, Redding, and Rossi-Hansberg (2018) for a formal proof of existence and uniquenessof the solution.

13

value for the strength of productivity spillovers to ν = 0.05. This implies that pro-ductivity increases by 3.5 percent if population doubles – a value that is in line withthe findings in Rosenthal and Strange (2004). The obtained regional productivityfundamentals are positively and strongly correlated with wages according to Figure3.

Figure 3: Wages and productivity

Productivity0.4

0.5

0.6

0.7

0.8

0.9

1.0

Wag

e

Notes: The figure shows correlation between the local productivity fundamentals Ān and regional wages at theworkplace wn. Note that productivity fundamentals are only determined up to scale, therefore we omit an explicitscale on the horizontal axis.

Price index, PQ,n. Using the results from above in (11) and normalizing the fixedlabor input requirement f to unity delivers values for local price indices.

Commuting cost parameter, µ. In a next step, we examine how workers valuecommuting to work. Our model helps us to answer this question. We start from thecommuting share equation

λni =Bni (τµniPαnQ1−αn )

−�w�i∑

r

∑sBrs (τµrsPαr Q1−αr )

−�w�s

and take logs on both sides to get

log λni = g0 + ηn + � logwi − µ� log τni + uni, (15)

where g0 is a constant term and ηn captures residence fixed effects. Notice that thescale parameters Bni that describe the average value households attach to living inn and working in i end up in the error term. Using round trip commuting times, τni,

14

Table 3: Commuting gravity estimation

log(commuting shares) OLS IV

(1) (2)

log(wage) 4.474∗∗∗ 5.046∗∗∗(0.125) (0.137)

log(commuting time) −3.756∗∗∗ −4.579∗∗∗(0.045) (0.051)

Constant −28.011∗∗∗ −28.591∗∗∗(1.107) (1.197)

Residence FE Yes Yes

R2 0.651 0.630

Observations 6,393 6,393

Notes: ∗∗∗, ∗∗, ∗ denote significance at the 1-, 5-, and 10-percent level, respec-tively.

as derived from google maps, (15) delivers estimated values for the Fréchet shapeparameter, �, and the commuting cost elasticity, µ.

To obtain unbiased estimates, one needs to assume that Bni is orthogonal to wagesand bilateral commuting times. This, however, is inconsistent with the notion ofa spatial model where location decisions of workers emerge endogenously basedon amenities, wages, and commuting times. We therefore amend the naive OLSregression with an instrumental variables approach where we use Euclidian distancesas instruments for commuting times τni.7 We further instrument for wages using ashift share IV strategy following Bartik (1991) or Baum-Snow and Ferreira (2015).We construct our instrument as a region-specific average wage by fixing industrycomposition in terms of employment shares for the year 1999 (the earliest yearfor which we have data). Assuming that regional wages in each industry grow atthe rate of the national industry average allows us to isolate shifts in local labordemand that come from national shocks in each sector of the economy. Variationacross space arises because regions differ in terms of their industry composition andthe exclusion restriction is satisfied as long as national shocks are uncorrelated withregional amenity levels.8

7We relegate results on the first stage to the appendix.8We thank Duncan Roth for providing us with the data.

15

Table 3 reports the results of both estimation approaches. We observe that higherwages at the place of work lead to higher commuting shares while longer commutesreduce the fraction of commuters. In particular, a one percent increase in the wagerate raises the commuting share by 4.5 percent in the OLS specification while a onepercent increase in commuting time reduces the commuting share by 3.8 percent.In the IV specification, the point estimates on wages and commuting time increasein absolute terms.

Amenities, Bni. Finally, we use bilateral trade shares to obtain a N × N systemof equations that solves for N × N values of Bni.9 This completes the calibrationexercise.

4 Eliminating traffic jams

We now utilize the model to understand the implications of rush hours for the spa-tial allocation of employment and population, average productivity and the housingmarket. Rather than haircutting bilateral commuting times by a certain share, weabolish location-specific traffic congestion by recomputing travel times between dis-tricts at 3 a.m. The idea is that traffic at that time is so low that even in the mosttraffic-prone locations there is no congestion. As locations are affected by trafficjams to different extents (see Table 1), we can expect heavily congested areas to re-spond in a more pronounced way than less congested areas with general equilibriumimplications for all locations. For the counterfactual, we also impute intra-districtcommuting times without traffic congestion following the same procedure as in thebaseline scenario. We compute for each region the average commuting time from allcontiguous districts, weighted by the number of workers commuting into the districtand take 20 percent of this value.

Figure 4 plots the distribution of travel times in a world without traffic jams (at3a.m.) relative to the travel time in a world with traffic congestion during rush hours(at 8a.m. and 5p.m. during weekdays). We observe that the reduction centers ataround −20% while there is quite a bit of heterogeneity across places. For themost traffic-prone regional commuting pairs an elimination of traffic jams reducescommuting times by more than 60%.

9See Figure 8 in the appendix for the geographical distribution of the calibrated amenities.

16

Figure 4: Reduction of commuting times

60 50 40 30 20 10 0Reductions in travel time, in percent

Notes: The figure shows the histogram of travel time reductions in percent if all traffic jams during rush hours wereabolished.

4.1 Spatial allocation of population and employment

Abolishing traffic congestion makes it more appealing to choose a place of residencewith low housing costs and a place of work offering high nominal income. In Table4, we use the classification of the Federal Institute for Research on Building, UrbanAffairs and Spatial Development in Germany to group districts according to popu-lation density and size. Large cities with more than 100,000 inhabitants form onegroup; three additional categories sort locations according to population density in“Mostly urban region”, “Mostly rural region” and “Rural region”.

We observe that locations in the two categories with the lowest density lose in termsof both population and employment. In contrast, the population share living inmostly urban regions and cities increases by 2.4 and 2.5 percentage points, respec-tively. The relative increase, though, is higher for mostly urban districts as theirpopulation shares are lower initially compared to cities. Employment, however, be-comes more concentrated in large cities because their commuting belts grow in termsof population and workers get better access to these high-wage places through com-muting. Taking the Gini-index as a measure of inequality, we find an increase withrespect to population from 0.39 to 0.45 and a more pronounced increase with respect

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Table 4: Rush hours and urbanization

Population share Employment share Average productivity

Region type Baseline Counterfactual Baseline Counterfactual Baseline Counterfactual

Large city 43.1 45.6 53.7 68.7 1.00 1.01

Mostly urban region 25.7 28.1 22.1 16.7 0.93 0.92

Mostly rural region 17.5 15.4 13.5 8.4 0.80 0.79

Rural region 13.7 10.9 10.6 6.2 0.76 0.74

Notes: We follow the type classification defined by the Federal Institute for Research on Building, Urban Affairsand Spatial Development. We classify regions consisting only of a city (kreisfreie Städte) and more than 100,000inhabitants as “Large city”. “Mostly urban region” denotes regions with a population density of more than 150inhabitants per square km. “Mostly rural region” refers to regions with population densities between 100 and 150inhabitants per square km. “Rural regions” are regions with less than 100 inhabitants per square km. Productivityis normalized to one in large cities in the baseline scenario, so that all productivity averages can be interpretedrelative to large cities.

to employment from 0.44 to 0.58.10 Although low-density districts with low housingcosts become relatively more attractive places of residence when traffic jams areabolished, it is not rural areas but “mostly urban region” that experience net immi-gration. In sum, traffic congestion during rush hours reduces both the economy-widedegree of urbanization and the agglomeration of employment. Further, the shareof cross-district commuters climbs from one third to 54 percent reflecting that traf-fic jams have a strong impact on the workplace-residence decision and operate asa significant friction in the spatial economy. It illustrates that commuting is animportant factor to understand spatial general equilibrium effects.

4.2 Labor productivity

The reason why the population in cities grows as well as in primarily urban areaswith lower housing costs roots in a combination of lower traffic congestion andhigher productivity. The last two columns in Table 4 reveal that cities are theonly type of regions that become more productive. We normalize productivity inlarge cities to unity and express productivity levels in all other categories relativeto this value. As productivity changes are positively associated with employmentchanges, all types of locations experience a decline in productivity except for largecities. More productive workers earn higher wages making high housing costs incities affordable for a larger fraction of households. Average productivity in cities

10Figures 9 and 10 in the appendix provide a graphical illustration of this finding.

18

grows by approximately 1 percent while it declines in the three remaining categoriesby 1-2 percentage points. Although productivity changes at the regional level aremoderate, average productivity in the economy increases by 7.2 percent. This isprimarily driven by the relocation of workers from less productive to more productiveplaces.

4.3 Housing market

Adjustments in residence and workplace decisions of households change both housingdemand and supply – the latter through changes in prices according to (7) – at thedistrict level. The response of regional house prices is very heterogeneous acrossspace. In districts experiencing net emigration, house prices are up to 27 percentlower in the new equilibrium. High-density locations, classified as “Large city” or“Mostly urban region” in Table 4 above, experience an average increase in housingcosts of 11.4% and 5.7%, respectively. The growth in cities is almost entirely drivenby the Ruhr Area – Europe’s largest conglomerate of urbanized areas (Schmidheinyand Suedekum 2015) – in Germany’s most populous state North Rhine-Westphaliathat suffers heavily from traffic congestion. If we take out all districts in NorthRhine-Westphalia, house prices in cities do not increase at all while mostly urbanregions experience an increase of 6%. Low density locations, classified as “Mostlyrural region” and “Rural region”, see an average decrease in housing costs of 9.3%and 18.7%, respectively. These changes translate to larger inequality of housingprices across space: the population-weighted Gini-index goes up from 0.72 to 0.79.

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Figure 5: The housing market in the Frankfurt region

Notes: The figure above depicts changes in house prices in our main specification of the counterfactual scenarioaround the city of Frankfurt. The color scheme is chosen, so that changes in house prices are grouped in quintilesover all districts in Germany.

In Figure 5, we take a closer look at the city of Frankfurt with its surroundingregions. We observe that, even though house prices might increase in the economiccenter when traffic congestion vanishes, the increase is much more pronounced inthe commuting belt around the city. Looking at this pattern alone shows that lowercommuting costs contribute to a convergence of house prices in this greater areabecause growth rates are higher in the commuting belt.

4.4 Robustness

To check the sensitivity of our conclusions with regard to the chosen parameter val-ues in the empirical exercise above, we undertake three robustness checks. First,we vary the weight on intra-district versus cross-district commuting. In the baselinecase, we have taken 20 percent of the weighted commuting times from neighboringdistricts as the measure for intra-district commuting time. We now vary this weight

20

between 0-40 percent. This is an important exercise because it affects the relativeattractiveness of places. For example, if we ignored intra-district commuting timealtogether, we would make adjacent districts relatively more attractive in the coun-terfactual implying higher net immigration there. Panel A in Table 5 supports thisintuition. Columns 1 and 2 report the counterfactual shares of population and em-ployment in “Large cities” or “Mostly urban regions” according to the classificationabove. Column 3 informs about the economy-wide average productivity change. Forthe sake of convenience, we repeat counterfactual results with the baseline parametervalues in bold. Reducing the weight to zero – implying no intra-district commutingtime – leads to a slightly lower population share and a slightly higher employmentshare. The reason is that the counterfactual makes location in neighboring regionsrelatively more attractive because commuting costs cannot decline within districtsby construction. Therefore, more workers locate outside of cities and commuteto high-wage jobs. As an immediate implication, the employment share in urbanregions increases which, in turn, translates into higher average productivity. The op-posite qualitative results emerge if we raise the share from 20 percent. Importantly,counterfactual outcomes do not respond much despite large changes in parametervalues.

As a second robustness check, we alter the truncation of travel times between dis-tricts. Compared to the baseline where we have included only round-trip traveltimes of up to three hours, truncating at 1 or 2 hours leads to lower productivitygains and lower agglomeration of employment and population. This is intuitive ashouseholds do not get the chance to commute longer distances by construction whichrules out gains from separation of place of work and place of residence. If we raisethe truncation to 4 hours, the results remain fairly stable.

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Table 5: Robustness of results

Panel A: Within district commuting

Urban population Urban employment ∅ Productivity

0% 73.5% 85.6% 7.7%

10% 73.6% 85.5% 7.4%

20% 73.7% 85.4% 7.2%

30% 73.8% 85.3% 6.9%

40% 74.0% 85.2% 6.6%

Panel B: Truncation of travel times

Urban population Urban employment ∅ Productivity

1h 71.2% 81.9% 4.0%

2h 73.3% 84.9% 6.7%

3h 73.7% 85.4% 7.2%

4h 73.5% 85.2% 7.0%

Panel C: Share of consumption expenditure

Urban population Urban employment ∅ Productivity

α = 0.7 73.7% 85.4% 7.2%

α = 0.8 76.0% 87.3% 9.1%

Notes: In all panels, the columns entitled “Urban population” and “Urban em-ployment” denote the share of workers living and working in “Large cities” and“Mostly urban regions” in our counterfactual scenario. The third column denotesthe increase in average productivity in the counterfactual. In our main specifi-cation, we use a value of 20 percent of the weighted bilateral commuting time ofneighbouring districts for intra-district commuting, a 3-hour threshold for traveltimes, and a share of consumption expenditure of 0.7. In each panel, we deviatefrom the main specification only in the respective dimension.

Finally, we reduce the expenditure share households dedicate to housing. In thebaseline, we have used 30 percent which included utilities and other housing-relateditems whose prices are not necessarily location-specific. Notice that the expenditureshare determines the strength of the congestion force in the model, so reducing the

22

share to 20 percent should favor agglomeration and thus higher productivity. Thisintuition is supported by Panel C of Table 5. Average productivity goes up byapproximately 2 percentage points, but the general insight that lower commutingtimes between districts raise economy-wide urbanization remains unaffected.

5 Conclusions

In this paper, we have explored the role of traffic congestion during rush hours for thespatial allocation of employment and population, average labor productivity and thehousing market. Intuitively, longer commutes to high-density, high-wage locationsmake it more attractive to either move to cities at the expense of higher housingcosts, or live and work in the countryside. Calibrating the model for Germanyshows, however, that an abolishment of traffic congestion stimulates immigrationto locations in the vicinity of economic centers that are within commuting distanceto high-wage locations. Therefore, traffic congestion reduces the degree of overallurbanization. Although living and working in high-wage places becomes a moreappealing option, congestion avoids urban sprawl in commuter belts.

Traffic jams therefore lead to a misallocation of workers across space as employmentis higher in less-productive places than in the absence of traffic jams. The modelsuggests that average labor productivity would be 7.2 percent higher in the absenceof traffic jams. The adjustment of workplace and residence choices also carries overto the housing market. While housing supply adjusts to price changes endogenouslyaccording to the housing supply elasticity, housing prices decline in districts ex-periencing net emigration while denser locations become more expensive places tolive.

Our results indicate that capacity-enhancing infrastructure investments generatehigher returns in cities and their commuter belts compared to peripheral regions.The reason for this stems from households changing low-productivity jobs in low-density places for high-paid jobs in economic centers.

23

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Appendix

A Solving the model in relative changes

We can solve for the relative changes in our model by solving the following systemof equations according to the iterative algorithm outlined in Monte, Redding, andRossi-Hansberg (2018):

Q̂n = ˆ̄vnR̂n

ˆ̄Hn

11+δŵiL̂iwiLi =

∑n

π̂niπni ˆ̄vnv̄nR̂nRn

P̂n =(L̂1−(1−σ)νnπ̂nn

) 11−σ d̂nnŵn

ˆ̄An

λ̂niλni =λniB̂ni

(P̂αn Q̂

1−αn

)−�(ŵi/κ̂ni)�∑

r

∑sλrsB̂rs

(P̂αr Q̂

1−αr

)−�(ŵs/κ̂rs)�

¯̂vnv̄n =∑i

λniB̂ni (ŵi/κ̂ni)�∑sλnsB̂ns (ŵs/κ̂ns)�

ŵiwi

R̂n =L̄

Rn

∑i

λniλ̂ni

L̂i =L̄

Li

∑n

λniλ̂ni

π̂niπni =πniL̂

1−(1−σ)νi

(d̂niŵi/

ˆ̄Ai)1−σ

∑kπnkL̂

1−(1−σ)νk

(d̂nkŵk/

ˆ̄Ak)1−σ

The system of equations above maps the model parameters {δ, σ, α, �}, the changes infundamentals { ˆ̄Hn, d̂ni, κ̂ni, B̂ni, Ân} and the observed current variables {wn, Ln, πni,v̄n, Rn, λni} into the relative changes in all model variables. For our elimination oftraffic jam we calculate κ̂ni = (τ ′ni/τni)

µ, where τ ′ni denotes google’s estimate oftravel time between n and i in the absence of traffic. We assume that the remainingfundamentals do not change.

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B First stage results

In this section, we present results of the first-stage regression of the IV-estimationof the distaste parameter for commuting, µ. Column (1) reports results for thepredicted values of wages while column (2) refers to travel time. The results indicatethat both instruments are valid.

Table 6: First stage regressions

Dependent variable Wage Travel time

(1) (2)

log(shift share wages) 0.563∗∗∗ 0.035∗∗∗(0.007) (0.013)

log(distance) −0.000 0.607∗∗∗(0.002) (0.004)

Constant 5.562∗∗∗ 2.236∗∗∗(0.045) (0.084)

Residence fixed effects Yes Yes

Observations 6,393 6,393

R2 0.789 0.809

F Statistic (df = 413; 5979) 54.164∗∗∗ 61.231∗∗∗

Notes: ∗∗∗, ∗∗, ∗ denote significance at the 1-, 5-, and 10-percent level, respectively.

C Data

In this appendix, we list detailed sources for the data we have used in the empiricalexercise:

• All data from the German Federal Employment Agency cover all employees inGermany that are employed in social security registered jobs. This includesregular full time employment, as well as apprenticeships, paid internships andstudent assistant jobs. It does not include part of state employees (Beamte)and self employed workers. The exact datasets used are listed below. Alldata cover the year 2010, the dates mentioned in the detailed data description

28

below indicates the date of the last official revision by the Federal EmploymentAgency.

– Regional employment and population: German Federal Employment Agency,Sozialversicherungspflichtig Beschäftigte nach ausgewählten Merkmalen,Nürnberg, Juni 2015.Employees residential addresses are reported by employers, when regis-tering a worker for social security with the Federal Employment Agency.Place of work is the location of the business unit within the company,where the employee actually works. Regional employment is the aggre-gate of registered workplaces over all districts. Regional population is theaggregate of registered residential addresses over all districts.

– Earnings by place of work and residence: German Federal EmploymentAgency, Sozialversicherungspflichtige Bruttoarbeitsentgelte, Entgeltstatis-tik 2014.Reported wages are before deduction of taxes and all social security pay-ments. Earnings by place of work are wages aggregate over regional em-ployment defined as above. Earnings by residence are wages aggregateover regional population defined as above.

– Commuting flows: German Federal Employment Agency, Sozialversich-erungspflichtig Beschäftigte - Pendler nach Kreisen, Nürnberg, Stichtag30. Juni 2014.Commuting flows use the same social security filings as regional employ-ment and population above, but are aggregated on bilateral pairs of work-place and residential districts instead. Bilateral pairs with less then 10commuters in total are omitted and set to zero.

• Regional land prices: German Federal Statistical Office, Statistik der Kaufw-erte für Bauland, EVAS-Nr.: 61511-01-03-4.Local tax offices collect information on all sales of undeveloped plots of landwith a size of at least 100 m2. The price per square meter is computed as thequotient of total sales price and and plot size.

• Bilateral trade flows: The trade flow matrix comes from the Forecast of Na-tionwide Transport Relations in Germany 2030 (VVP). It covers trade flows(in metric tons) that either have a German NUTS-3 region as origin or desti-nation or serve as a transit region for intra-European trade of regions outsideof Germany. The data distinguish between the mode of transport, namely

29

road, rail, and water, and product groups according to NST2007. For rail andwater, the data come from the German Federal Statistical Office and for roadfrom the Federal Motor Transport Authority (Kraftfahrtbundesamt). Loca-tions trade flows are reported at the NUTS-3 level. The data were collected ina project undertaken by Intraplan Consulting, Munich, in collaboration withBVU Consulting, Freiburg, for the Federal Ministry of Transport and Digi-tal Infrastructure and is only available for 2010. The data are made availablethrough the Institute for Transport Research of the German Aerospace Center.

• Language similarity: We use the index of language similarity in Germany forall NUTS-3 regions constructed by Lameli et al. (2015). The index is based ona comprehensive language survey of more then 40,000 German schools in thelate 19th century by the linguist Georg Wenker. A more detailed discussion ofthe survey can be found in Lameli (2013). The similarity index is constructedby comparison of 66 language characteristics between regions.

• Geographic information: German Federal Agency for Cartography and Geodesy,District definition for the year 2010. The German Federal Agency for Cartog-raphy and Geodesy provieds shape files for all administrative units in Germanyfor different points in time. The file that we use uses a scale of 1:250. Theemployed projection is a Transverse Mercator projection (WGS 1984, UTMzone 32).

• Classification of districts: The definition follows Federal Institute for Researchon Building, Urban Affairs and Spatial Developmenthttps://www.bbsr.bund.de/BBSR/DE/Raumbeobachtung/Raumabgrenzungen/Kreistypen4/kreistypen.html?nn=443270As the regional classification from the institute is not available for years priorto 2015 we use a similar method on our regions for the year 2010. We clas-sify regions consisting only of a city (kreisfreie Städte) and more than 100,000inhabitants as “Large city”. “Primarily urban” denotes regions with popula-tion density of more than 150 inhabitants per square km. “Primarily rural”refers to regions with population densities between 100 and 150 inhabitantsper square km. “Rural regions” are regions with less than 100 inhabitants persquare km.

30

https://www.bbsr.bund.de/BBSR/DE/Raumbeobachtung/Raumabgrenzungen/Kreistypen4/kreistypen.html?nn=443270https://www.bbsr.bund.de/BBSR/DE/Raumbeobachtung/Raumabgrenzungen/Kreistypen4/kreistypen.html?nn=443270

D Figures

Figure 6: Round-trip travel times between home and work

0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0Hours

Notes: The figure shows round trip travel times for all combinations of districts by car. We take the centroid ofeach district and compute travel times at 8 a.m. and 5 p.m. from google maps.

31

Figure 7: Average absolute time spent in traffic

Note: Time spent in traffic is computed as the average difference between rush hour travel time and traffic freetravel time, weighted by the number of workers commuting into a region.

32

Figure 8: Average Amenities in residential locations

Notes: Residential amenities are computed as an employment weighted sum over all estimated bilateral amenitiesBni.

33

Figure 9: Regional changes in employment

Notes: Color scheme is ordered in quintiles of the distribution of relative employment changes.

34

Figure 10: Regional changes in population

Notes: Color scheme is ordered in quintiles of the distribution of relative population changes.

35

Seidel rush_hours_submit.pdfIntroductionModelWorkersHousing marketProduction and inter-regional tradeEquilibrium

Data and calibrationDataCalibration

Eliminating traffic jamsSpatial allocation of population and employmentLabor productivityHousing marketRobustness

ConclusionsSolving the model in relative changesFirst stage resultsDataFigures

7587abstract.pdfAbstract